Evaluate lim f(x)

Question

f(x)=10–12x+6x²–x³

 

Evaluate: lim f(x)

               x→^–∞

 

 

              lim f(x)

               x→⁺∞

Answer 1

f(x)=10–12x+6x²–x³ is a polynomial, so the behavior of f(x) as x tends to ⁺∞ or to ⁻∞ depends on both the leading coefficient and the polynomial degree.

f(x) has degree 3, so the ends of the function tend in opposite directions. Since the coefficient on x³ is −1, this tells us the right end of f(x) ultimately decreases.

lim f(x) = ⁻∞

_{x→ +∞}

and

lim f(x) = ⁺∞

_{x→ -∞}